Where did I go wrong? (exponents)

This question involved finding one side length of a rectangle given that the diagonal length = 12cm and the perimeter = 28cm. I got the correct answer in the end using a different equation (the equation for diagonal length) but the first thing I tried to do was to be "clever" with exponents and I got a nonsense answer. I'm just interested to see what lovely stupid mistake I made :s

It's nonsense because $\sqrt{a^2 - b^2} \not\equiv a-b$.

Yeah, I was suspecting that was what I'd done (that's why I crossed it out the first time) but then what is 2(12^2 - x^2)^1/2 equal to? Is that its simplest form? Thanks

You can't expand any expressions in the form $(a \pm b)^n$, with non-integer exponents, as far as you know. (even then, expansions are only valid under certain circumstances) You should, when attempting to solve an equation, "remove" the square root by squaring, rather than attempt to expand it

Are you trying to solve $2x + 2\sqrt{144-x^2} = 28$? Start by dividing both sides by two, and then see what you can do from there, noting the above.